One related problem is the forward reachability analysis, where we deal with uncertain system with no control inputs (e.g., closed-loop systems), and compute the set of states that can be visited in the future from some initial state in a given set \(X_0\) , under a certain disturbance profile.
Such forward reachable sets can be computed offline for system verification, and online for state prediction.
Often times, the forward reachable sets are overestimated for robustness.
For linear systems, a special polyhedron called zonotope is widely used to represent forward reachable sets due to its favorable computational complexity under linear transformation (for forward state evolution) and Minkowski addition (to account for additive uncertainty). For example, see [1]}, [2]}.
Algorithms that compute zonotopic forward reachable sets are much more scalable than those dealing with general polyhedra.
